In a conventional internal combustion engine automobile, the functions of a clutch are: making the automobile starts stably; interrupting the power supply to the transmission apparatus to assist gear-position shifting; and preventing from overloading on the transmission apparatus. However, the implement for above functions with clutch not only requires the driver to operate skillfully but also causes power interruption inevitably; as a result, the acceleration/deceleration of the automobile is not smooth enough. In addition, the clutch operates by utilizing the friction on contact surfaces between drive part and driven part, utilizing liquid as driving medium or utilizing magnetic force for driving; therefore, the clutch has aging and wearing problems. Furthermore, in a hybrid automobile or electric automobile, since the motor can start the automobile with loads, the startup procedure doesn't need a clutch used in traditional internal combustion engine automobiles. Therefore, when designing a transmission apparatus for hybrid automobile or electric automobile, it is desired that to design a clutchless transmission apparatus and a control method to adapt for the intrinsic characteristics of motor, rather than to improve traditional transmission apparatuses in prior arts, such as the gear-position shifting control method used in a clutchless variable speed operated parallel hybrid automobiles as disclosed in CN1272203C.